Work in progress. Unfortunately the maze is not always solvable - the limit on back-forward is the real hurdle.
Edit 1 Cosmetic
Edit 2 Better gameplay, but the big problem is still there
Beatnik, 733 bytes
Since it really had to be done, here it is. It was a really nasty to debug and provided a few challenges.
Input must be uppercase letters only.
Output is unary (hope that is OK?)